In this paper we examine the inverse problem of determining the length of a one-dimensional bar from thermal measurements (temperature and heat flux) at one end of the bar (the "accessible" end); the other inaccessible end of the bar is assumed to be moving. We develop two different approaches to estimating the length of the bar, and show how one approach can also be adapted to find unknown boundary conditions at the inaccessible end of the bar.
Yarlikina, Natalya and Walrath, Holly, "Determining the Length of a One-Dimensional Bar" (2004). Mathematical Sciences Technical Reports (MSTR). 41.